Hi. Are you referring to a movement that's like "hitoemi"? One where your shoulders stay over your hips as you move? I was still a little unclear on your description.
In general, though, I agree with Gerardo, Chris, and Chris. I typically don't have shoulders and hips moving as one, nor do I initiate movement with the hips. With weapons, I've been shown why that is a bad thing.
As a training tool ... again, I personally wouldn't do that. But, I have heard that a "hitoemi" type of movement can generate some strength/power.
Ok...I am exploring an idea...Endo Sensei really demonstrated it nicely...sorry my description was so scketchy....writing about it can be hard. I think I am saying one thing until I get it reflected back at me and then see I have said another.
Thanks for the video, Graham.